GROUND WATER CONTAMINATION

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• GROUND WATER CONTAMINATION

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A MATLAB OPTIMIZATION EXAMPLE

• function ssemy_function(x)
• my_function is defined in
• file my_function.m
• global Cobs t
• kx(1)
• Cox(2)
• CpCoexp(-kt)
• ssenorm(Cp-Cobs)

• load 'ex1.dat'
• global Cobs t
• Cobsex1(,2)
• tex1(,1)
• x00 6
• xfinalfmins('my_function',x0)
• subplot 121
• hold off
• plot(t, Cobs, '')
• ylabel('Concentration (mg/L)')
• xlabel('Time (hours)')
• kxfinal(1)
• Coxfinal(2)
• CpCoexp(-kt)
• hold on
• plot(t, Cp)
• subplot 122
• semilogy(t, Cobs, '')
• axis(0 20 0.1 15)

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CALIBRATION OF MATLAB MODELS

• Define an objective function Fobj(x) where x is
  the set of parameters to be estimated
• Yobs can not be transfer to Fobj as argument.
  Use global variables
• Fobj calls the model Y(x)
• Use the minimization subroutine fmins to minimize
  Fobj(x) as a function of x
• If the above steps do not work, use EXCEL.

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McDonalds gas
Industrial site
Leaking petroleum tank
Farmer house
Pond
Municipal water well
Leakage from hazardous waste site
Accidental fuel spill
Infiltration of fertilizers and pesticides
Ocean
Septic tank leakage
water table
Saline water
Mechanisms of ground water contamination
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3-D TRANSPORT IN THE SATURATED ZONE (Steady State
Solution)
dH/dy0

• Example
• Well contamination problem
• Gauss Seidel (Succesive over relaxation)

dH/dx0
H0
dH/dy0
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3-D TRANSPORT IN THE SATURATED ZONE
dH/dy0

• Example
• Kinzelbachs example
• Rectangular confined 700 x 700 m2 aquifer
• 7 by 7 nodes
• K 0.1 m2 s-1 and storage coefficient S 0.001.
• Discharge well is located in node (4,4) Q 1 m3
  s-1
• Boundary conditions H 50 m at west and east
  boundary and no-flow boundary at north and at
  south.

Q1m3s-1
H50m
H50m
dH/dy0
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3-D TRANSPORT IN THE SATURATED ZONE
dH/dy0
H50m
Q1m3s-1
H50m
j
j-1
i
i1
dH/dy0
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MATLAB SOLUTION OF GROUNDWATER TRANSPORT EQUATION

• k0.1 S0.001 dx50 dt1.5
• cdt/dx2k/S Q1.0 r-Q/dx2
• hin50 n700/dx holdzeros(n2,n)hin
  hnewhold
• for it180
• Set the boundary condition
• hold(n2,)hnew(n1,)
• hold(1,)hnew(2,)
• for i2n1
• for j2n-1
• hnew(i,j)hold(i,j)c(hold(i-1,j)hold(i,j-
  1)-4hold(i,j) ...
• hold(i1,j)hold(i,j1))
• if i fix((n3)/2) j fix((n1)/2)
• hnew(i,j)hnew(i,j)rdt/S
• end
• end
• end
• holdhnew
• end

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MATLAB SOLUTION OF GROUNDWATER TRANSPORT EQUATION
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WRAP-UP

• Excel is not as silly as it seems
• However, a more advance use of Excel requires
  programming (or automatization)
• Transient ground water modeling may be readily
  achieved using standard numerical methods